Arnold's seminar
December 5th, 2000

Klaus Mohnke's proof of Arnold's chord conjecture
Yuri Chekanov

A contact form gives rise to the Reeb vector field, which
is the contact vector field defined by contact Hamiltonian 1.
A chord is a piece of Reeb trajectory connecting two points
on a Legendrian submanifold. (A version of) the famous
Arnold's chord conjecture claims that for each contact form
defining the standard contact structure on the odd-dimensional
sphere and each closed Legendrian submanifold, there exists
a chord with ends on the submanifold. This conjecture, with
generalizations to certain other contact manifold, has been
recently proved by Klaus Mohnke. His proof will be presented
in the talk.